Banach空间中极大单调算子扰动的值域
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摘要
设X为实Banach空间，T：D(T)E→2~(X~*)为极大单调算子，C：D(T)E→X~*为有界算子(未必连续)，而C(T+J)~(-1)为紧算子。本文在上述假设条件下，通过附加一定的边界条件应用Leray-Schauder度理论研究了下述包含关系：以及(其中SX~*)；以及(其中BX~*，DX~*)的可解性，得出了一些新的结论。
Let X is a real Banach space, T : D(T) E - 2X* is a maximal monotone operator, C : D(T) E - X* is a bounded operator (but not bound to continuous), while C(T + J)-1 is a compact operator. On the conditions of above, this paper studies the solvability of the following including relationships by adding certain boundary conditions and making use of Leray-Schauder
degree theory: 0 (T + C)(D(T) BQ(0)), 0 (T + C)(D(T) BQ(0))- and
S R(T + C), intS intR(T + C)(where S X*); and B + D R(T + C), int(B + D)cintfl(T + C)(here B X*, D X*) ; Based on this, we derive some new conclusions.
Let X is a real Banach space, T : D(T) E - 2X* is a maximal monotone operator, C : D(T) E - X* is a bounded operator (but not bound to continuous), while C(T + J)-1 is a compact operator. On the conditions of above, this paper studies the solvability of the following including relationships by adding certain boundary conditions and making use of Leray-Schauder
degree theory: 0 (T + C)(D(T) BQ(0)), 0 (T + C)(D(T) BQ(0))- and
S R(T + C), intS intR(T + C)(where S X*); and B + D R(T + C), int(B + D)cintfl(T + C)(here B X*, D X*) ; Based on this, we derive some new conclusions.
引文
1. Z.Guan and A.G.Kartsatos, Range of perturbed maximal monotone and maccretive operators in Banach spaces[J].Tran.Amer.Math.Soc. Vol 347,1995.
2. Zeider E., Nonlinear funtional analysis and its applications[M].Vol Ⅱ(B),nonlinear monotone operators,Spinger Verlag. Berlin,1990.
3. A.G.kartsatos, New results in the perturbation theory of m-accretive operators in Banach spaces [J].Tran.Amer.Math.Soc. 1996,348(3):1663-1707.
4．周海云，A．G．Kartsatos，Banach空间中带扰动的m-增生算子的零点与映象定理[J]．系统科学与数学，2001，21(4)：446-454．
5．何震，伪单调算子紧扰动的值域[J]．应用泛函分析学报．2000，2(3)．
6. Barbu.V., Nonlinear semigroups and evolution equations in Banach spaces[J]. Noorhoff, Leyden. (1978).
7. Dan Pa.scali and Silviu Sburlan, Nonlinear mappings of monotone type[M]. Editura Academiei, Bucuresti,Romania.(1978).
8．赵义纯，非线性泛函分析及其应用[M]．高等教育出版社．
9. Z.Guan, Ranges of operators of monotone type in Banach spaces[J]. Math.Anal. Appl. 174(1993),256-264.MR 95b:47068.
10. Z.Guan and A.G.Kartsatos, On the eigenvalue problem for perturbation of nonlinear accretive and monotone operators in Banach spaces[J]. Nonlinear Anal. (to appear).
2. Zeider E., Nonlinear funtional analysis and its applications[M].Vol Ⅱ(B),nonlinear monotone operators,Spinger Verlag. Berlin,1990.
3. A.G.kartsatos, New results in the perturbation theory of m-accretive operators in Banach spaces [J].Tran.Amer.Math.Soc. 1996,348(3):1663-1707.
4．周海云，A．G．Kartsatos，Banach空间中带扰动的m-增生算子的零点与映象定理[J]．系统科学与数学，2001，21(4)：446-454．
5．何震，伪单调算子紧扰动的值域[J]．应用泛函分析学报．2000，2(3)．
6. Barbu.V., Nonlinear semigroups and evolution equations in Banach spaces[J]. Noorhoff, Leyden. (1978).
7. Dan Pa.scali and Silviu Sburlan, Nonlinear mappings of monotone type[M]. Editura Academiei, Bucuresti,Romania.(1978).
8．赵义纯，非线性泛函分析及其应用[M]．高等教育出版社．
9. Z.Guan, Ranges of operators of monotone type in Banach spaces[J]. Math.Anal. Appl. 174(1993),256-264.MR 95b:47068.
10. Z.Guan and A.G.Kartsatos, On the eigenvalue problem for perturbation of nonlinear accretive and monotone operators in Banach spaces[J]. Nonlinear Anal. (to appear).